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Chapter 9: Problem 102

The thyroid hormone thyroxine has the molecular formula \(\mathrm{C}_{15} \mathrm{H}_{11} \mathrm{NO}_{4} \mathrm{I}_{4} .\) Calculate the mass percent of each element in thyroxine.

Short Answer

Expert verified
The mass percent of each element in Thyroxine is approximately: Carbon: 23.18%, Hydrogen: 1.43%, Nitrogen: 1.80%, Oxygen: 8.23%, and Iodine: 65.3%.

Step by step solution

01

Determining the molar mass of Thyroxine

To determine the molar mass of Thyroxine, we need to sum the atomic masses of all the elements in the compound, multiplied by the number of atoms of each element in the molecular formula: \(\mathrm{C}_{15}\mathrm{H}_{11}\mathrm{NO}_{4}\mathrm{I}_{4}\). Molar mass of Thyroxine = (15 × atomic mass of C) + (11 × atomic mass of H) + (1 × atomic mass of N) + (4 × atomic mass of O) + (4 × atomic mass of I) Using the atomic masses from the periodic table: C = 12.01 g/mol H = 1.01 g/mol N = 14.01 g/mol O = 16.00 g/mol I = 126.90 g/mol Molar mass of Thyroxine = (15 × 12.01) + (11 × 1.01) + (1 × 14.01) + (4 × 16.00) + (4 × 126.90) Molar mass of Thyroxine ≈ 776.87 g/mol
02

Calculate the mass contribution of each element

Next, we need to calculate the mass contribution of each element in the compound: Mass contribution of Carbon = 15 × 12.01 = 180.15 g/mol Mass contribution of Hydrogen = 11 × 1.01 = 11.11 g/mol Mass contribution of Nitrogen = 1 × 14.01 = 14.01 g/mol Mass contribution of Oxygen = 4 × 16.00 = 64.00 g/mol Mass contribution of Iodine = 4 × 126.90 = 507.60 g/mol
03

Calculate the mass percent of each element

Finally, we can calculate the mass percent of each element by dividing the mass contribution of that element by the total molar mass of Thyroxine and multiplying by 100: Mass percent of Carbon = (180.15/776.87) × 100 ≈ 23.18% Mass percent of Hydrogen = (11.11/776.87) × 100 ≈ 1.43% Mass percent of Nitrogen = (14.01/776.87) × 100 ≈ 1.80% Mass percent of Oxygen = (64.00/776.87) × 100 ≈ 8.23% Mass percent of Iodine = (507.60/776.87) × 100 ≈ 65.3% So, the mass percent of each element in Thyroxine is approximately: Carbon: 23.18% Hydrogen: 1.43% Nitrogen: 1.80% Oxygen: 8.23% Iodine: 65.3%

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